First move analysis here....second move analysis is basically done but just trying to verify that some of the clusters I identify are correct. Discrepancies are 0 because you can't really have variations on a single move (since we are already accounting for moves that are essentially identical differing only by board rotation or reflection).

It looks like Cluster 6 (h1-h3) gives the best results for black. The balance looks about the same for the overall game balance

Second move analysis should be up tomorrow or the following day if all goes well
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Cluster Number 1 White Win %: 76.0 Black Win % 24.0 Draw % 0.0 Number of games: 21 Median Discrepancy: 0.0

Here's a sample of the first two moves assuming we have started with h1-h3 (or an equivalent move). I'm going to insert the figures and try and have the whole document posted. There are more countermoves in response to h1-h3 but these are the most interesting to me.

Also I updated my code to only generate clusters that have 0 variation. It causes a few changes, but nothing terribly significant.

We know from statistics that it's harder for black to win. Best black opening move gives black a chance of 43%. Other openings are available but more challenging, chance 24%.

Answering the "best black opening move", white has a choice of three answers, which don't spoil white's chance of winning, i.e. the chance still being >= 50%.

While I think that's the general sense of it, there are some caveats. I just put together the full document for responses to h1-h3 and mailed it to you and there are many options available to white which preserve white's advantage. There are many others that do not. If white makes the wrong move here the outcome could be disastrous.

I think I need to do one more level of analysis of blacks response to white's best move in this sequence. I suspect at least one black move will flip the odds in black's favor or at least preserve them near equality, as we know there are multiple board configurations at 4 moves where black has the advantage from my previous analysis.

Also, even the best odds for black here actually aren't that different from 56-43 white to black. Which is the default win probability from the first move. Because we are looking at a subset of moves given h1-h3. So say even a 70% win probability from this point out is only 70% of a smaller set of games than the entire set of games examined...The actual win probability as measure from the beginning of the game may not change much.

Brench wrote: I just put together the full document for responses to h1-h3 and mailed it to you and there are many options available to white which preserve white's advantage. There are many others that do not. If white makes the wrong move here the outcome could be disastrous.

Brench wrote: I just put together the full document for responses to h1-h3 and mailed it to you and there are many options available to white which preserve white's advantage. There are many others that do not. If white makes the wrong move here the outcome could be disastrous.

And one of white's winning answers looks like a monster move; after this one white has 83% chance of winning! (cluster 17)

That cluster is intruiging, although it's only 23 games. A shift of just 5 games converts that into a 60% chance, which is more in line with the overall game balance. It would be interesting to have several masters play a tournament each other *starting from that configuration* to see if any new responses to that opening could be developed for black...

A general trend: the larger the cluster, the closer you get to the overall game balance.

One thing I haven't examined, but should is the GAME length after a given opening. The longer a game goes on, the less the opening probably matters as the board gets decorrelated from the initial positions.

I think if we can show that there is always a decent response by black to any move by white (so if white makes a move and bumps the white win probability to 80% say and then black makes a move to bring it down to around 60%) the game is about as balanced as it can be (or should be...white's advantage makes this game more inherently interesting to me than chess).

Brench wrote:That cluster is intruiging, although it's only 23 games. A shift of just 5 games converts that into a 60% chance, which is more in line with the overall game balance. It would be interesting to have several masters play a tournament each other *starting from that configuration* to see if any new responses to that opening could be developed for black...

In a few weeks I'll set up a test tournament, asking players to start with the cluster 17 two moves.